{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e017c9a3",
   "metadata": {},
   "source": [
    "# Learning to stabilize a linear system\n",
    "\n",
    "For this example we demonstrate learning to stabilize a double integrator system using [Differentiable predictive control (DPC) method](https://www.sciencedirect.com/science/article/pii/S0959152422000981). \n",
    "\n",
    "**Differentiable Predictive Control method**:  \n",
    "The DPC is a model-based policy optimization algorithm, that exploits the differentiability of a wide class of model representations for dynamical systems, including differential equations, state-space models, or various neural network architectures. In DPC, we construct a differentiable closed-loop system composed of neural control policy and system dynamics model that is to be optimized using parametric control objectives as intrinsic reward signals evaluated over a sampled distribution of the problem parameters.\n",
    "\n",
    "<img src=\"./figs/DPC_simple_method.png\" width=\"600\">  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff3ffdcd",
   "metadata": {},
   "source": [
    "## NeuroMANCER and Dependencies"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bac7825",
   "metadata": {},
   "source": [
    "### Install (Colab only)\n",
    "Skip this step when running locally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa12921d",
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install neuromancer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54e902d0",
   "metadata": {},
   "source": [
    "*Note: When running on Colab, one might encounter a pip dependency error with Lida 0.0.10. This can be ignored*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1a9b6ec8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from neuromancer.system import Node, System\n",
    "from neuromancer.modules import blocks\n",
    "from neuromancer.dataset import DictDataset\n",
    "from neuromancer.constraint import variable\n",
    "from neuromancer.loss import PenaltyLoss\n",
    "from neuromancer.problem import Problem\n",
    "from neuromancer.trainer import Trainer\n",
    "from neuromancer.plot import pltCL, pltPhase"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfe1b7ed",
   "metadata": {},
   "source": [
    "# Node and System classes\n",
    "\n",
    "The Node class is a simple wrapper for any callable pytorch function or nn.Module which provides names for the inputs and outputs to be used in composition of a potentially cyclic computational graph.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cd824de1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Double integrator parameters\n",
    "nx = 2\n",
    "nu = 1\n",
    "A = torch.tensor([[1.2, 1.0],\n",
    "                  [0.0, 1.0]])\n",
    "B = torch.tensor([[1.0],\n",
    "                  [0.5]])\n",
    "\n",
    "# linear state space model\n",
    "xnext = lambda x, u: x @ A.T + u @ B.T    \n",
    "double_integrator = Node(xnext, ['X', 'U'], ['X'], name='integrator')\n",
    "\n",
    "# neural control policy\n",
    "mlp = blocks.MLP(nx, nu, bias=True,\n",
    "                 linear_map=torch.nn.Linear,\n",
    "                 nonlin=torch.nn.ReLU,\n",
    "                 hsizes=[20, 20, 20, 20])\n",
    "policy = Node(mlp, ['X'], ['U'], name='policy')\n",
    "\n",
    "# closed loop system definition\n",
    "cl_system = System([policy, double_integrator])\n",
    "# cl_system.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa938158",
   "metadata": {},
   "source": [
    "# Training dataset generation\n",
    "\n",
    "For a training dataset we randomly sample points away from the origin of the 2D space the system operates in. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b74ee8c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training dataset generation\n",
    "train_data = DictDataset({'X': 3.*torch.randn(3333, 1, nx)}, name='train')  # Split conditions into train and dev\n",
    "dev_data = DictDataset({'X': 3.*torch.randn(3333, 1, nx)}, name='dev')\n",
    "train_loader = torch.utils.data.DataLoader(train_data, batch_size=3333,\n",
    "                                           collate_fn=train_data.collate_fn, shuffle=False)\n",
    "dev_loader = torch.utils.data.DataLoader(dev_data, batch_size=3333,\n",
    "                                         collate_fn=dev_data.collate_fn, shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0387d6a2",
   "metadata": {},
   "source": [
    "# Optimization problem\n",
    "\n",
    "We want to learn a controller that stabilizes the double integrator system. In other words we would like a control policy that pushes the system to stay at the origin. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "149f7bc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define optimization problem\n",
    "u = variable('U')\n",
    "x = variable('X')\n",
    "action_loss = 0.0001 * (u == 0.)^2  # control penalty\n",
    "regulation_loss = 10. * (x == 0.)^2  # target position\n",
    "loss = PenaltyLoss([action_loss, regulation_loss], [])\n",
    "problem = Problem([cl_system], loss)\n",
    "optimizer = torch.optim.AdamW(policy.parameters(), lr=0.001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb5ef578",
   "metadata": {},
   "source": [
    "# Optimize problem with a system rollout of 2 time steps\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9467aec0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "epoch: 249  train_loss: 39.7130126953125\n",
      "epoch: 250  train_loss: 39.712982177734375\n",
      "epoch: 251  train_loss: 39.71296310424805\n",
      "epoch: 252  train_loss: 39.71293258666992\n",
      "epoch: 253  train_loss: 39.712913513183594\n",
      "epoch: 254  train_loss: 39.71288299560547\n",
      "epoch: 255  train_loss: 39.712860107421875\n",
      "epoch: 256  train_loss: 39.71283721923828\n",
      "epoch: 257  train_loss: 39.71281814575195\n",
      "epoch: 258  train_loss: 39.712791442871094\n",
      "epoch: 259  train_loss: 39.712764739990234\n",
      "epoch: 260  train_loss: 39.71274185180664\n",
      "epoch: 261  train_loss: 39.71272277832031\n",
      "epoch: 262  train_loss: 39.71269607543945\n",
      "epoch: 263  train_loss: 39.712677001953125\n",
      "epoch: 264  train_loss: 39.7126579284668\n",
      "epoch: 265  train_loss: 39.712646484375\n",
      "epoch: 266  train_loss: 39.71261978149414\n",
      "epoch: 267  train_loss: 39.71260070800781\n",
      "epoch: 268  train_loss: 39.712581634521484\n",
      "epoch: 269  train_loss: 39.712562561035156\n",
      "epoch: 270  train_loss: 39.712547302246094\n",
      "epoch: 271  train_loss: 39.712528228759766\n",
      "epoch: 272  train_loss: 39.7125129699707\n",
      "epoch: 273  train_loss: 39.71249771118164\n",
      "epoch: 274  train_loss: 39.71248245239258\n",
      "epoch: 275  train_loss: 39.712467193603516\n",
      "epoch: 276  train_loss: 39.712459564208984\n",
      "epoch: 277  train_loss: 39.712459564208984\n",
      "epoch: 278  train_loss: 39.71247482299805\n",
      "epoch: 279  train_loss: 39.7125244140625\n",
      "epoch: 280  train_loss: 39.712615966796875\n",
      "epoch: 281  train_loss: 39.7127571105957\n",
      "epoch: 282  train_loss: 39.712982177734375\n",
      "epoch: 283  train_loss: 39.71321105957031\n",
      "epoch: 284  train_loss: 39.71345901489258\n",
      "epoch: 285  train_loss: 39.713417053222656\n",
      "epoch: 286  train_loss: 39.7131462097168\n",
      "epoch: 287  train_loss: 39.71261978149414\n",
      "epoch: 288  train_loss: 39.71221923828125\n",
      "epoch: 289  train_loss: 39.71214294433594\n",
      "epoch: 290  train_loss: 39.71231460571289\n",
      "epoch: 291  train_loss: 39.712547302246094\n",
      "epoch: 292  train_loss: 39.71260070800781\n",
      "epoch: 293  train_loss: 39.712467193603516\n",
      "epoch: 294  train_loss: 39.71219253540039\n",
      "epoch: 295  train_loss: 39.71202087402344\n",
      "epoch: 296  train_loss: 39.712032318115234\n",
      "epoch: 297  train_loss: 39.71217346191406\n",
      "epoch: 298  train_loss: 39.712284088134766\n",
      "epoch: 299  train_loss: 39.71223449707031\n",
      "epoch: 300  train_loss: 39.71208572387695\n",
      "epoch: 301  train_loss: 39.7119255065918\n",
      "epoch: 302  train_loss: 39.71186447143555\n",
      "epoch: 303  train_loss: 39.71189498901367\n",
      "epoch: 304  train_loss: 39.71195983886719\n",
      "epoch: 305  train_loss: 39.71199035644531\n",
      "epoch: 306  train_loss: 39.7119255065918\n",
      "epoch: 307  train_loss: 39.71182632446289\n",
      "epoch: 308  train_loss: 39.71174240112305\n",
      "epoch: 309  train_loss: 39.71171188354492\n",
      "epoch: 310  train_loss: 39.71171951293945\n",
      "epoch: 311  train_loss: 39.71174240112305\n",
      "epoch: 312  train_loss: 39.71174240112305\n",
      "epoch: 313  train_loss: 39.71170425415039\n",
      "epoch: 314  train_loss: 39.71163558959961\n",
      "epoch: 315  train_loss: 39.71156311035156\n",
      "epoch: 316  train_loss: 39.71150588989258\n",
      "epoch: 317  train_loss: 39.71146774291992\n",
      "epoch: 318  train_loss: 39.71144485473633\n",
      "epoch: 319  train_loss: 39.711429595947266\n",
      "epoch: 320  train_loss: 39.7114143371582\n",
      "epoch: 321  train_loss: 39.711387634277344\n",
      "epoch: 322  train_loss: 39.711360931396484\n",
      "epoch: 323  train_loss: 39.711341857910156\n",
      "epoch: 324  train_loss: 39.71133041381836\n",
      "epoch: 325  train_loss: 39.7113151550293\n",
      "epoch: 326  train_loss: 39.71131134033203\n",
      "epoch: 327  train_loss: 39.711299896240234\n",
      "epoch: 328  train_loss: 39.71128845214844\n",
      "epoch: 329  train_loss: 39.711280822753906\n",
      "epoch: 330  train_loss: 39.71126937866211\n",
      "epoch: 331  train_loss: 39.71125793457031\n",
      "epoch: 332  train_loss: 39.71124267578125\n",
      "epoch: 333  train_loss: 39.71123123168945\n",
      "epoch: 334  train_loss: 39.71122360229492\n",
      "epoch: 335  train_loss: 39.71121597290039\n",
      "epoch: 336  train_loss: 39.71120071411133\n",
      "epoch: 337  train_loss: 39.71118927001953\n",
      "epoch: 338  train_loss: 39.7111701965332\n",
      "epoch: 339  train_loss: 39.711177825927734\n",
      "epoch: 340  train_loss: 39.711177825927734\n",
      "epoch: 341  train_loss: 39.711185455322266\n",
      "epoch: 342  train_loss: 39.711185455322266\n",
      "epoch: 343  train_loss: 39.71118927001953\n",
      "epoch: 344  train_loss: 39.71118927001953\n",
      "epoch: 345  train_loss: 39.71118927001953\n",
      "epoch: 346  train_loss: 39.7111701965332\n",
      "epoch: 347  train_loss: 39.711158752441406\n",
      "epoch: 348  train_loss: 39.71112823486328\n",
      "epoch: 349  train_loss: 39.71110916137695\n",
      "epoch: 350  train_loss: 39.71107482910156\n",
      "epoch: 351  train_loss: 39.711036682128906\n",
      "epoch: 352  train_loss: 39.71100616455078\n",
      "epoch: 353  train_loss: 39.71097183227539\n",
      "epoch: 354  train_loss: 39.71094512939453\n",
      "epoch: 355  train_loss: 39.710914611816406\n",
      "epoch: 356  train_loss: 39.71089172363281\n",
      "epoch: 357  train_loss: 39.710872650146484\n",
      "epoch: 358  train_loss: 39.710853576660156\n",
      "epoch: 359  train_loss: 39.71083450317383\n",
      "epoch: 360  train_loss: 39.710819244384766\n",
      "epoch: 361  train_loss: 39.7108039855957\n",
      "epoch: 362  train_loss: 39.710792541503906\n",
      "epoch: 363  train_loss: 39.71078109741211\n",
      "epoch: 364  train_loss: 39.71077346801758\n",
      "epoch: 365  train_loss: 39.71076202392578\n",
      "epoch: 366  train_loss: 39.710750579833984\n",
      "epoch: 367  train_loss: 39.71073913574219\n",
      "epoch: 368  train_loss: 39.710731506347656\n",
      "epoch: 369  train_loss: 39.71072006225586\n",
      "epoch: 370  train_loss: 39.71072006225586\n",
      "epoch: 371  train_loss: 39.71071243286133\n",
      "epoch: 372  train_loss: 39.71072006225586\n",
      "epoch: 373  train_loss: 39.710731506347656\n",
      "epoch: 374  train_loss: 39.710777282714844\n",
      "epoch: 375  train_loss: 39.710853576660156\n",
      "epoch: 376  train_loss: 39.711029052734375\n",
      "epoch: 377  train_loss: 39.71133804321289\n",
      "epoch: 378  train_loss: 39.71192169189453\n",
      "epoch: 379  train_loss: 39.71269226074219\n",
      "epoch: 380  train_loss: 39.71381378173828\n",
      "epoch: 381  train_loss: 39.71403884887695\n",
      "epoch: 382  train_loss: 39.713260650634766\n",
      "epoch: 383  train_loss: 39.7114143371582\n",
      "epoch: 384  train_loss: 39.7105827331543\n",
      "epoch: 385  train_loss: 39.711299896240234\n",
      "epoch: 386  train_loss: 39.712242126464844\n",
      "epoch: 387  train_loss: 39.71224594116211\n",
      "epoch: 388  train_loss: 39.711116790771484\n",
      "epoch: 389  train_loss: 39.71055221557617\n",
      "epoch: 390  train_loss: 39.7110481262207\n",
      "epoch: 391  train_loss: 39.71151351928711\n",
      "epoch: 392  train_loss: 39.71120071411133\n",
      "epoch: 393  train_loss: 39.71058654785156\n",
      "epoch: 394  train_loss: 39.71061325073242\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 395  train_loss: 39.711036682128906\n",
      "epoch: 396  train_loss: 39.7110710144043\n",
      "epoch: 397  train_loss: 39.710693359375\n",
      "epoch: 398  train_loss: 39.71046829223633\n",
      "epoch: 399  train_loss: 39.710670471191406\n"
     ]
    }
   ],
   "source": [
    "trainer = Trainer(\n",
    "    problem,\n",
    "    train_loader,\n",
    "    dev_loader,\n",
    "    dev_loader,\n",
    "    optimizer=optimizer,\n",
    "    epochs=400,\n",
    "    train_metric=\"train_loss\",\n",
    "    dev_metric=\"dev_loss\",\n",
    "    eval_metric='dev_loss',\n",
    "    warmup=400,\n",
    ")\n",
    "\n",
    "# Train model with prediction horizon of 2\n",
    "cl_system.nsteps = 2\n",
    "best_model = trainer.train()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c1360ed",
   "metadata": {},
   "source": [
    "# Evaluate best model on a system rollout \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "937b9143",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2000x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test best model with prediction horizon of 50\n",
    "problem.load_state_dict(best_model)\n",
    "data = {'X': torch.ones(1, 1, nx, dtype=torch.float32)}\n",
    "nsteps = 30\n",
    "cl_system.nsteps = nsteps\n",
    "trajectories = cl_system(data)\n",
    "pltCL(Y=trajectories['X'].detach().reshape(nsteps+1, 2), U=trajectories['U'].detach().reshape(nsteps, 1), figname='cl.png')\n",
    "pltPhase(X=trajectories['X'].detach().reshape(nsteps+1, 2), figname='phase.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd18fbb3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f59b909f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "neuromancer",
   "language": "python",
   "name": "neuromancer"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
